Isoperimetric Inequality for Disconnected Regions

Bidyut Sanki; Arya Vadnere

doi:10.1007/s10711-024-00961-9

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arXiv · 1908.07697

Isoperimetric Inequality for Disconnected Regions

Bidyut Sanki·Arya Vadnere

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Abstract

The discrete isoperimetric inequality in Euclidean geometry states that among all $n$-gons having a fixed perimeter $p$, the one with the largest area is the regular $n$-gon. The statement is true in spherical geometry and hyperbolic geometry as well. In this paper, we generalize the discrete isoperimetric inequality to disconnected regions, i.e. we allow the area to be split between regions. We give necessary and sufficient conditions for the result (in Euclidean, spherical and hyperbolic geometry) to hold for multiple $n$-gons whose areas add up.

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BibTeX RIS

Bidyut Sanki, Arya Vadnere. 2019-08-21. Isoperimetric Inequality for Disconnected Regions. https://doi.org/10.1007/s10711-024-00961-9

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